Q4/ If z = Vx² – y² and x increasing at 3.5 m/s, determine at what rate y must change in order that z shall be neither increasing nor decreasing at the instant x = 5 m and y = 3 m.

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A: Given that,The acceleration of the particle is 10t for t ≥ 0.The particle reached at the distance of…

Q: A particle moves along the curve below. y = sqt(24 + x^3) As it reaches the point (1, 5), the…

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Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: Solution :-

Q: A tank that can hold 500 gal. originally contains 200 gal. of water with 100 Ibs. of salt in…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Suppose that z ry where bothx and y are changing withtime At acertain instant whernr= 2 and y = 1…

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Q: consider a tree with a tr

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Q: A 600 litre tank initially contains 200 litres of water in which 10 grams of salt are dissolved.…

A: (a) A 600 litre tank initially contains 200 liters of water. 10 grams of salt are dissolved in it.…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

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Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

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Q: In order to stay awake during class, a professor keeps a 200 ounce capacity coffee maker in his…

A: Given coffee maker capacity is 200 ounces. it contains 40 ounces coffee which has 500 mg caffeine.…

Q: A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1…

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Q: m Oil is running into an inverted conical tank at the rate of 37 -. If the min tank has a radius 2.5…

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Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: 4. The organism amoebus rectilineus always maintains the shape of a right triangle whose area is 10°…

A: 4. Consider a right angled triangle: Here, Hypotenuse=hHeight=aBase=b   Given: Area of triangle A…

Q: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

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Q: A particle is moving along the curve y = 2+ Vx + 1. At the instant that the partical passes through…

A: (15) Find dy/dt from y using the chain rule and dx/dt from the statement given.

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

A: Given initial quantity of freshwater in the 200-gallon tank = 100 gallons At t=0, salt solution is…

Q: John is an epidemiologist. He is tasked to determine the rate at which the total average of COVID…

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Q: A point P is moving along the line whose equation is y =2x. How fast is the distance between P and…

A: The line is given by y=2x, differentiate w. r. t. t to get: dydt=2dxdt Let Px,y be a point on the…

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

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Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two…

A: The radius is 2 times the height, the rate at which the height increases is 3 cm/s when the pile is…

Q: A point P is moving along the line whose equation is y 2x. How fast is the distance between P and…

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Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

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Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Now in triangle ABC, by using Pythagorean theorem, we get

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

Q: Let I be the length of a diagonal of a rectangle whose sides have lengths a and y, and assume that a…

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Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1lb of…

A: Given that a 50 gal tank initially contains 10 gals of fresh water.

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

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Q: Suppose that a car starts from rest, its engine providing an acceleration of 10 ft/s², while air…

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Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: A particle is moving along the curve y = x². As the particle passes through the point (1,e), its…

A: Given: A particle is moving along the curve y=x2. As the particle passes through the point (1, e),…

Q: The side of an equilateral triangle is increasing at a rate of 3 m/sec, then the rate at which its…

A: Let the side of an equilateral triangle be x cm.∴ Area of equilateral triangle, A = √3/4x2…

Q: A tank contains 1000 liters (L) of a solution consisting of 100 kg of salt dissolved in water. Pure…

A: Consider, is the Rate of pure water is pumped into the tank is equal to 5 L/s. Formula used,

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

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Q: A point P is moving along the line whose equation is y = 2x. How fast is the distance between P and…

A: Firstly we find the distance between a random point on the line y = 2x, and then we differentiate…

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

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Q: Let / be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

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Q: If a ball is thrown vertically upward and with an initial velocity of 10 m/s, it’s velocity at the…

A: To find: The velocity at the highest point reached by the stone. Given: The initial velocity of the…

Q: A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 1b…

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Q: A point P is moving along the curve whose equation is  y=4x. How fast is the distance between P and…

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Q: 4. Consider a lake of constant volume 12200 km³, which at time t contains an amount y(t) tons of…

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Q: A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution  containing 1…

A: It is given that a 50 gallon tank initially contains 10 gallon fresh water. A brine solution with 1…

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Given that,  'L' be the length of a diagonal of a rectangle whose sides have lengths x and y, and x…

Q: When the price of a certain commpdity is p dollars per unit, the manufacturer is willing to supply x…

A: Given  5p2 - 2x2 = 27 where p is the price of a certain commodity in dollars per unit x is the…

Q: - Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = 2 (all…

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Q: A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of…

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Q: A 50-gallon tank initially contains 10 gallons of fresh water. At t= 0, a brine solution containing…

A: We will find out the required time.